Maxwell Garnett approximation in random media: tutorial

In the third part of the tutorial, we develop a Maxwell Garnett approximation, which is applicable, in particular, to disordered random media with non-spherical inclusions and to multicomponent mixtures. We are especially interested in the case when the inclusions are non-spherical and randomly distributed and oriented in space, but the composite is isotropic on average. The effective medium formula applicable to such media cannot be obtained by direct generalization of the results that were derived in the first two parts of the tutorial. We show that the Maxwell Garnett effective medium approximation can be stated in a very general form. The results derived by us previously as well as a result applicable to the medium described above can be obtained as special cases of this general result.